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Zbl 0955.37022
Agiza, H.N.
On the analysis of stability, bifurcation, chaos and chaos control of Kopel map. (English)
[J] Chaos Solitons Fractals 10, No.11, 1909-1916 (1999). ISSN 0960-0779

The author deals with the Cournot duopoly problem, that is $$\aligned x_{t+1} &= (1-\rho)x_t+ \rho\mu y_t(1- y_t),\\ y_{t+1} &= (1-\rho)y_t+ \rho\mu x_t(1-y_t) \endaligned \tag 1$$ where $\rho,\mu\in \bbfR_+$, $x_t$ and $y_t$ are production quantities. Here the author is interested only in positive solutions. He provides conditions for the stability of the fixed points and studies the bifurcation and chaos for (1), by computing the maximum Lyapunov exponents. Control of chaos is also discussed.
[Messoud Efendiev (Berlin)]

MSC 2000:: *37E30 Homeomorphisms and diffeomorphisms of planes and surfaces
37N40 Dynamical systems in optimization and economics
37C75 Stability theory
37D45 Strange attractors, chaotic dynamics
37C35 Orbit growth
65P30 Bifurcation problems

Keywords: stability; bifurcations; chaos control; Kopel map

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Zentralblatt MATH Berlin [Germany]